BRAGG REFLECTION OF SHALLOW-WATER WAVES ON A SLOPING BEACH

Yong-Sik Cho, Jong-In Lee, Jong-Kyu Lee

Abstract

In this study a set of governing equations describing the evolution of modulated shallow-water waves over a sinusoidally varying topography on a sloping beach is derived. The governing equations include the nonlinear interactions among different wave components as well as the shoaling effect over a slowly varying topography. It has been shown that the incident waves could be resonantly reflected by the interaction with the rippled seabed under the Bragg reflection condition. The magnitude of the resonantly reflected wave is almost equal to those of the incident and the transmitted waves.